Details

Time bar (total: 3.0m)

sample99.0ms

Algorithm
intervals
Results
35.0ms210×body80valid
13.0ms14×body1280valid
13.0ms256×pre80true
12.0ms18×body640valid
4.0ms7×body320valid
2.0ms7×body160valid

simplify171.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
171.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize37.0ms

Local error

Found 3 expressions with local error:

21.9b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.1b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite813.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
83×*-un-lft-identity
43×add-sqr-sqrt add-cube-cbrt
42×fma-def
24×associate-/r/
20×distribute-lft-out
17×add-cbrt-cube add-exp-log
16×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp
5×add-log-exp
4×frac-times
3×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Counts
3 → 162
Calls
3 calls:
Slowest
601.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
156.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
51.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series888.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
461.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
322.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
105.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify37.3s

Counts
171 → 171
Calls
171 calls:
Slowest
723.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
688.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
681.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ 1 (+ (+ alpha beta) (* 2 i))))
669.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
666.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize62.0ms

Local error

Found 3 expressions with local error:

10.9b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
162×*-un-lft-identity
118×add-sqr-sqrt
80×add-cube-cbrt
26×associate-/l*
22×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
10×add-cbrt-cube add-exp-log
7×associate-/r* flip3-+ flip-+ div-inv
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 div-sub insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×clear-num frac-2neg
1×flip3-- fma-udef flip--
Counts
3 → 184
Calls
3 calls:
Slowest
172.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
31.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
1.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series774.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
454.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
224.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
95.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify1.0m

Counts
296 → 193
Calls
296 calls:
Slowest
1.2s
(exp (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
955.0ms
(/ (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
854.0ms
(/ (/ (- (sqrt beta) (sqrt alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
837.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
793.0ms
(/ (/ (sqrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

localize62.0ms

Local error

Found 4 expressions with local error:

10.9b
(fma (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ beta alpha) 1.0)
3.8b
(log (fma (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ beta alpha) 1.0))
0.2b
(exp (log (fma (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ beta alpha) 1.0)))
0.1b
(/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
151×times-frac
142×*-un-lft-identity
102×add-sqr-sqrt
72×add-cube-cbrt
20×distribute-lft-out
19×associate-/l*
15×distribute-lft-out-- difference-of-squares
10×add-exp-log
9×add-cbrt-cube
6×pow1 log-prod div-inv
4×expm1-log1p-u exp-prod associate-/r* insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp exp-sum
2×div-sub associate-/r/ log-pow
1×clear-num frac-2neg flip3-+ rem-log-exp flip-+ fma-udef rem-exp-log associate-/l/
Counts
4 → 164
Calls
4 calls:
Slowest
23.0ms
(/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha))))
5.0ms
(exp (log (fma (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ beta alpha) 1.0)))
2.0ms
(log (fma (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ beta alpha) 1.0))
1.0ms
(fma (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ beta alpha) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
421.0ms
(log (fma (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ beta alpha) 1.0))
268.0ms
(/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha))))
257.0ms
(exp (log (fma (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ beta alpha) 1.0)))
253.0ms
(fma (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ beta alpha) 1.0)

simplify51.4s

Counts
258 → 176
Calls
258 calls:
Slowest
1.3s
(* (* (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))))
875.0ms
(* (* (fma (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ beta alpha) 1.0) (fma (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ beta alpha) 1.0)) (fma (/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ beta alpha) 1.0))
670.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
628.0ms
(/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (- (* 2.0 2.0) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))
627.0ms
(/ (/ (- beta alpha) (fma 2 i (+ beta alpha))) (+ (pow 2.0 3) (pow (fma 2 i (+ beta alpha)) 3)))

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

localize70.0ms

Local error

Found 4 expressions with local error:

10.9b
(fma (/ (/ (+ alpha beta) 1) 1) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×fma-udef
Counts
4 → 62
Calls
4 calls:
Slowest
50.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
47.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
43.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
366.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
219.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
214.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
203.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))

simplify12.3s

Counts
89 → 74
Calls
89 calls:
Slowest
300.0ms
(* (/ (/ (+ alpha beta) 1) 1) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
280.0ms
(* (* (fma (/ (/ (+ alpha beta) 1) 1) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0) (fma (/ (/ (+ alpha beta) 1) 1) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)) (fma (/ (/ (+ alpha beta) 1) 1) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0))
256.0ms
(real->posit16 (fma (/ (/ (+ alpha beta) 1) 1) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0))
252.0ms
(exp (fma (/ (/ (+ alpha beta) 1) 1) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0))
247.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

regimes329.0ms

Accuracy

12.1% (5.4b remaining)

Error of 11.4b against oracle of 6.0b and baseline of 12.1b

bsearch112.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s6408×body80valid
869.0ms586×body640valid
407.0ms463×body1280valid
364.0ms8000×pre80true
147.0ms341×body320valid
63.0ms202×body160valid